Sullivan Algebra and Trigonometry: Section 12.8

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Presentation transcript:

Sullivan Algebra and Trigonometry: Section 12.8 Objectives of this Section Graph an Inequality Graph a System of Linear Inequalities

An inequality in two variable x and y is satisfied by an ordered pair (a,b) if, when x is replaced by a and y by b, a true statement results. A graph of an inequality in two variables x and y consists of all points (x,y) whose coordinates satisfy the inequality.

Steps For Graphing an Inequality Step 1: Replace the inequality symbol with an equal sign and graph the resulting equation. If the inequality is strict, use dashes; if it is non-strict, use a solid line. This graph separates the xy-plane into two (or more) regions. Step 2: In each of the regions, select a test point P. a. If the coordinates of P satisfies the inequality, then so do all the points in the region. Indicate this by shading the region. b. If the coordinates of P do not satisfy the inequality, then no points in the region do.

2x - y -8 > 0 Test point: (1, 3) Test point: (5, 1) 2(1) - 3 - 8 = -9 < 0 Does not belong to graph Test point: (5, 1) 2(5) - 1 - 8 = 1 > 0 Belongs to graph

y = 2x - 8 5 -10

Graph x - y = 6 y = x - 6 Graph 4x + 2y = 10 2y = -4x + 10 y = -2x + 5

y = x - 6 y = -2x + 5

Test Point: (0, 0) x - y > 6 0 - 0 > 6 NO, shade side opposite (0, 0). 4x + 2y < 10 4(0) + 2(0) < 10 Yes, shade side containing (0, 0).

y < -2x + 5 y > x - 6